Did you see the pattern?

Algebra Level 4

Given that p(x)p(x) is a monic quartic polynomial such that p(1)=2p(1)=2, p(2)=5p(2)=5, p(3)=10p(3)=10, p(4)=17p(4)=17.

Determine the value of p(5)p(5).

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